Question

The sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their square.

Answer 1

Let a, b be the two numbers.
.'. a + b = 7 and a³ + b³ = 133
(a + b)³ = a³ + b³ + 3ab (a + b)

⇒ (7)³ = 133 + 3ab (7)
⇒ 343 = 133 + 21ab
⇒  21ab = 343 - 133 = 210
⇒ 21ab = 210
⇒ ab= 10

Now a² + b² = (a + b)² - 2ab
                     = 7² - 2 x 10 = 49 - 20 = 29